Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 216 · 40 questions

How to solve it (Divide by 7 first): Circle: circumference = 2 × π × r; area = π × r × r. With π = 22/7, divide the radius by 7 first. Cube of edge a: volume = a × a × a, surface area = 6 × a × a. Cuboid: volume = l × b × h, surface area = 2 × (lb + bh + hl). Make every length k times as long: areas become k × k times as big, volumes k × k × k times.

1. 1.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
2. 2.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
3. 3.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 2464 cm (d) 88 cm
4. 4.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
5. 5.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 616 sq cm
6. 6.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 9 times (c) 3 times (d) 6 times
7. 7.A cuboid is 6 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 126 sq cm (b) 324 sq cm (c) 162 sq cm (d) 81 sq cm
8. 8.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 64 times (c) 4 times (d) 16 times
9. 9.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
10. 10.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 4 times (b) 8 times (c) 2 times (d) 5 times
11. 11.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq cm
12. 12.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 132 cm (d) 1386 cm
13. 13.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 486 sq cm (c) 324 sq cm (d) 81 sq cm
14. 14.A cube has edges of 10 cm. What is its volume? (a) 30 cu cm (b) 600 cu cm (c) 1000 cu cm (d) 400 cu cm
15. 15.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
16. 16.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 66 cm (d) 1386 cm
17. 17.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 343 sq cm (c) 49 sq cm (d) 294 sq cm
18. 18.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 22 cm (d) 88 cm
19. 19.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
20. 20.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 8 cu cm (c) 24 cu cm (d) 6 cu cm
21. 21.A cuboid is 8 cm long, 5 cm wide and 3 cm high. What is its volume? (a) 158 cu cm (b) 40 cu cm (c) 120 cu cm (d) 16 cu cm
22. 22.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
23. 23.A cuboid is 9 cm long, 7 cm wide and 8 cm high. What is its total surface area? (a) 504 sq cm (b) 764 sq cm (c) 382 sq cm (d) 191 sq cm
24. 24.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
25. 25.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 132 sq cm (d) 5544 sq cm
26. 26.A cuboid is 10 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 100 sq cm (b) 80 sq cm (c) 320 sq cm (d) 160 sq cm
27. 27.A cuboid is 7 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 21 cu cm (b) 84 cu cm (c) 14 cu cm (d) 122 cu cm
28. 28.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
29. 29.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 10 times (c) 125 times (d) 5 times
30. 30.A cube has edges of 9 cm. What is its volume? (a) 486 cu cm (b) 27 cu cm (c) 729 cu cm (d) 324 cu cm
31. 31.A cuboid is 11 cm long, 10 cm wide and 6 cm high. What is its volume? (a) 472 cu cm (b) 110 cu cm (c) 660 cu cm (d) 27 cu cm
32. 32.A cuboid is 5 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 12 cu cm (b) 20 cu cm (c) 60 cu cm (d) 94 cu cm
33. 33.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 8 times (c) 2 times (d) 6 times
34. 34.A cube has edges of 12 cm. What is its total surface area? (a) 144 sq cm (b) 864 sq cm (c) 1728 sq cm (d) 576 sq cm
35. 35.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 54 cu cm (c) 36 cu cm (d) 27 cu cm
36. 36.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
37. 37.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 9856 sq cm
38. 38.A cuboid is 10 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 164 sq cm (b) 82 sq cm (c) 120 sq cm (d) 328 sq cm
39. 39.A cuboid is 12 cm long, 4 cm wide and 5 cm high. What is its volume? (a) 256 cu cm (b) 48 cu cm (c) 240 cu cm (d) 21 cu cm
40. 40.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 64 times (c) 16 times (d) 4 times

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